Geometry, Mechanics, and Electronics of Singular Structures and Wrinkles in Graphene
Abstract
Vitor M. Pereira and A. H. Castro Neto*
Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
H. Y. Liang and L. Mahadevan*
School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, Massachusetts 02138, USA
Received 12 May 2010; published 5 October 2010
As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity, and electronics at the limits of their validity. We describe the transport and electronic structure in the neighborhood of conical singularities, the elementary excitations of the ubiquitous wrinkled and crumpled graphene. We use a combination of atomistic mechanical simulations, analytical geometry, and transport calculations in curved graphene, and exact diagonalization of the electronic spectrum to calculate the effects of geometry on electronic structure, transport, and mobility in suspended samples, and how the geometry-generated pseudomagnetic and pseudoelectric fields might disrupt Landau quantization.
© 2010 The American Physical Society
URL: http://link.aps.org/doi/10.1103/PhysRevLett.105.156603
DOI: 10.1103/PhysRevLett.105.156603
PACS: 72.80.Vp, 61.48.Gh, 62.20.-x
*
Phys. Rev. Lett. 105, 156801 (2010) [4 pages]
Effective Magnetic Fields in Graphene Superlattices
Abstract
Jianmin Sun and H. A. Fertig
Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
L. Brey
Instituto de Ciencia de Materiales de Madrid (CSIC), Cantoblanco 28049, Spain
Received 4 June 2010; published 5 October 2010
We demonstrate that the electronic spectrum of graphene in a one-dimensional periodic potential will develop a Landau level spectrum when the potential magnitude varies slowly in space. The effect is related to extra Dirac points generated by the potential whose positions are sensitive to its magnitude. We exploit a chiral symmetry in the Dirac Hamiltonian description with a superlattice potential to show that the low energy theory contains an effective magnetic field. Numerical diagonalization of the Dirac equation confirms the presence of Landau levels. Possible consequences for transport are discussed.
© 2010 The American Physical Society
URL: http://link.aps.org/doi/10.1103/PhysRevLett.105.156801
DOI: 10.1103/PhysRevLett.105.156801
PACS: 73.22.Pr, 72.80.Vp, 73.21.Cd